linear equations
Difficulty Levels:
1
Q&A
Basic
Write down the equation of line $$L$$ in the form $$y=m x+c$$．[1]
$$y=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .$$
Answer:
$$y=3 x-2$$ oe
Explanation:
FT their（a）
2
Q&A
Basic
Rovers，United and City are football teams．
Rovers scored $$x$$ goals．United scored 8 goals more than Rovers．City scored 3 goals less than twice the number of goals scored by Rovers．
The three teams scored a total of 117 goals．
Write down and solve an equation to find the value of $$x$$．[4]
$$x=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .$$
Answer:
$$x+x+8+2 x-3=117$$ or better
$$4 x+5=117$$ oe or better
28
Explanation:
or B1 for $x+8$ or $2 x-3$
If 0 scored，$\mathbf{S C} 1$ for the correct answer with no algebra
3
CHOICE
Basic
Tom's age is $$T$$ years，which is also the sum of the ages of his three children．His age $$N$$ years ago was twice the sum of their ages then．What is $$T/N$$？( )
Answer:
D
Explanation:
Tom's age $N$ years ago was $T-N$．The sum of the ages of his three children $N$ years ago was $T-3 N$，since there are three children．If his age $N$ years ago was twice the sum of the children's ages then，
$$
\begin{aligned}
T-N &=2(T-3 N) \\
T-N &=2 T-6 N \\
T &=5 N \\
T / N &=(\mathrm{D}) 5
\end{aligned}
$$
Note that actual values were not found．
4
CHOICE
Basic
The equations $$2x + 7 = 3$$ and $$bx - 10 = - 2$$ have the same solution．What is the value of $$b$$？( )
Answer:
B
Explanation:
$2 x+7=3 \Longrightarrow x=-2, \quad-2 b-10=-2 \Longrightarrow-2 b=8 \Longrightarrow b=-4(\mathrm{~B})$
5
CHOICE
Basic
Let $$f$$ be a linear function for which $$f(6) - f(2) = 12.$$ What is $$f(12) - f(2)?$$ ( )
Answer:
D
Explanation:
Since $f$ is a linear function with slope $m$，
$$
\begin{gathered}
m=\frac{f(6)-f(2)}{\Delta x}=\frac{12}{6-2}=3 \\
f(12)-f(2)=m \Delta x=3(12-2)=30 \Rightarrow(D)
\end{gathered}
$$
